The invention relates to a process for controlling a pipe-cutting arrangement in a continuously operating pipe-forming machine for forming wound pipes made of bands of sheet material. The invention also pertains to an arrangement for carrying out the afore-described process. Continuously operating pipe-winding arrangements are already known in the art. In particular, spiral winding machines are known which include a sled reciprocally mounted along the wound pipe which carries a cutting member. The velocity of the axial displacment of the sled equals the advancing speed of the pipe during the cutting process. Such known arrangement furthermore includes feeler means which sense the position of the end of the pipe and thereby terminate the cutting process (see for example German published patent application No. 2 612 795). This known arrangement includes a pipe velocity measuring circuit for avoiding a permissible marking of the lengthwise measurement on the pipe. This pipe velocity measuring circut includes a plurality of photocells and a variable time-delay member which effects a delay of the starting signal coming from the feeler for the cutting arrangement in dependence from the scanned pipe velocity.